The vehicles' Autopilot system generates a speed limit warning on the dashboard display and sends a notification if the car is sitting still at a green traffic light.
The features were released in the latest update of Tesla's "full self-driving" version of Autopilot.
Tesla vehicles can already slow down at red lights and stop signs.
In July 2019, Tesla's website advertised the "full potential for autonomous driving" including automatic driving on motorways - although it has always maintained that its Autopilot is not designed to be a substitute for a human driver.
Previous Tesla models have had speed-limit sign recognition, which was enabled by the firm's former business partner Mobileye.
Between 2013 and 2016, the Israeli maker of camera sensors and software supplied Tesla with technology for the Autopilot feature used in its Model S and Model X vehicles. But in July 2016, the companies ended the relationship, citing the first reported Autopilot fatality as a factor.
Owners of cars built under the partnership had complained road signs were sometimes inaccurately interpreted. Vehicles would not register a speed limit sign at all or drive at excessive speeds, reported Tesla blog, Teslerati.
Tesla's latest software update applies to Autopilot cars made after 2016, which are not fitted with Mobileye cameras.
Elsewhere, Cruise - the self-driving car start-up, majority-owned by General Motors - has said it is using artificial intelligence to train cars to understand bike users and pedestrians' body language.
This could be used to identify somebody holding their hand up to signal stop, or a cyclist extending their left arm to indicate they are turning left, for example.
The firm detailed its methods in an article for the Institute of Electrical and Electronics Engineers.